Problem: In polar coordinates, the point $\left( -2, \frac{3 \pi}{8} \right)$ is equivalent to what other point, in the standard polar coordinate representation?  Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$
Answer: To obtain the point $\left( -2, \frac{3 \pi}{8} \right),$ we move counter-clockwise from the positive $x$-axis by an angle of $\frac{3 \pi}{8},$ then take the point with $r = -2$ at this angle.  Since $-2$ is negative, we end up reflecting through the origin.  Thus, we arrive at the point $\boxed{\left( 2, \frac{11 \pi}{8} \right)}.$

[asy]
unitsize(1 cm);

draw(Circle((0,0),2),red);
draw((-2.5,0)--(2.5,0));
draw((0,-2.5)--(0,2.5));
draw((0,0)--((-2)*dir(67.5)));
draw((0,0)--(2*dir(67.5)),dashed);

dot((-2)*dir(67.5));
dot(2*dir(67.6));

label("$\frac{3 \pi}{8}$", (0.5,0.3));
[/asy]